Is a/c necessary in Vienna in August? I know last year was brutally hot all over Europe.
I just got back from being in Vienna June 10-13, when they were experiencing a bit of a heat wave and it got to be 85-90 degrees those days. After one night in an unairconditioned pension, we switched to a hotel with AC. Unlike in the US, you can't duck into a restaurant or shop and get rejuvenated by the AC. Nothing has AC, from the palaces to Starbucks! I think we would have covered a lot less ground had we not been able to go back to the hotel for a half hour of cold air. And we were two 24 year old girls who were traveling on a budget, so we weren't terribly picky when it came to hotel amenities, but AC was some of the best money we spent. If you're sensitive to heat, go for it.
It was very hot in Salzburg and Vienna. We are staying at the Ibis in Vienna. They are air conditioned. That is my first priority. I learned the hard way. Ditto restaurants.
Yes, your comfort and rest is imp. it will be the best euros spent.
I agree with JS, having done Vienna in July. It can be really hot and when you spend all day walking around the city in the heat you'll be thankful for a cool room to crash in.